PROBABILITY 1. Random experiment: An experiment is said to be random if all possible outcomes of the experiment are known but the exact outcome can not be pericted in advance.
PROBABILITY
2. Sample space : The set of all possible outcomes of an experiment is known as sample space and it is usally denoted by S.The sample space of tossing a coin is S ={H,T}and the sample space of tossing two coins at a time is S= {HT,TH,TT,HH} and the sample space of rolling a die is S ={1,2,3,4,5,6}.and n(s) represent the number of outcomes of a sample space inS.when a die is rolled twice, then n(s)=6power 2 = 36.Each outcomes of sample space is called Sample point. There are two types of sample spaces namely discrete and continus
DisCrete – when elements are countable.
Continuous – when elements are not countable.
3. TRAIL AND EVENT:To Perform an experiment is known as trial and possible outcomes of the experiment is called event .for example rolling a dice or tossing a coin any number of times is trial and turning up head or tail or occurrence of numbers 1,2,3,4,5,6 are events .so every subset of a sample space is an event.
TYPES OF EVENT
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Simple event: An event is said to be simple if it contains only one elememt in sample space.
Compound event: An event is said to be a compound event it having more than one element in sample space.
Eqally likely event or equally probable event:Events are said to be equally likely if there is no reason for an event to occur in preference to any other event .It means events are said to be equally likely when each event is equally likely to occur as any other.
MUTUALLY EXCLUSIVE EVENTS:Two or more than two events are said to be mutually exclusive if the occurrence any one of them exclude/ruled out the occurrence of the other .The events A1,A2…….An are mutually exhaustive if Ai intersection Aj= Empty
EXHAUSTIVE EVENTS: The events A ,B C……X,Y,Z are said to be exhaustive events ,if there Union is sample space
As .S= {1,2,3,4,5,6}. and A={1,3,5} ,B={2,4,6}
Then A Union B equal is S.
MUTUALLY EXCLUSIVE AND EXHAUSTIVE EVENTS: Let S be sample space.Then the events are said to be mutually exclusive and EXHAUSTIVE if their intersection is 0 and their union is sample space.
INDEPENDENT EVENTS: Events A and B are said to be independent if happening or non happining of A does not effect the happining or non happining of B .
PROBABILITY
DEPENDENT EVENT.
S: Two or more than two events are said to be dependent if happening of one effects the happining of other .For example , drawing two card from a deck of card without replacement.
COMPLEMENT OF AN EVENT : The set of all outcomes which are in S but not in A is called complement of A which is denoted by A’ and A’= S-A
IMPOSSIBLE EVENT: Event which do not consist any element of sample space is called impossible event . Throwing a die and hope to obtain head or tail is impossible.
PROBABILITY
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